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This paper considers the occurrence of explosive resonant triads in fluid mechanics. These are weakly nonlinear waves whose amplitudes become unbounded in finite time. Previous work is expanded to include interfacial flow systems with continuously varying basic velocities and densities. The first paper in this series [10] discussed the surprisingly strong singular nature of explosive triads. Many of the problems to be studied here will be found to have additional singularities, and the techniques for analyzing these difficulties will be developed. This will involve the concept of a critical layer in a fluid, a level at which a wave phase speed equals the unperturbed fluid velocity in the direction of propagation. Examples of such waves in this context are presented.

In this paper, a collection of results pertaining to resonant triads in fluid flow systems is presented. The main topic is the extension of the analysis by Mahoney for wind-driven shear flows to general, layered flows, that is to say, flows which have piecewise continuous velocity and density profiles. It is seen how the results for calculating the triad interaction coefficients for two-layer flows generalize and carry over for multilayer flows.

In the linear inviscid theory of shear flow stability, the eigenvalue problem for a neutral or weakly amplified mode revolves around possible discontinuities in the eigenfunction as the singular critical point is crossed. Extensions of the linear normal mode approach to include nonlinearity and/or wave packets lead to amplitude evolution equations where, again, critical point singularities are an issue because the coefficients of the amplitude equations generally involve singular integrals. In the past, viscosity, nonlinearity, or time dependence has been introduced in a critical layer centered upon the singular point to resolve these integrals. The form of the amplitude evolution equation is greatly influenced by which choice is made. In this paper, a new approach is proposed in which wave packet effects are dominant in the critical layer and it is argued that in many applications this is the appropriate choice. The theory is applied to two-dimensional wave propagation in homogeneous shear flows and also to stratified shear flows. Other generalizations are indicated.